Zebras, like many other equids, lack the 'domestication' gene that was bred into horses over 1000 years or so. As I understand it, the problem was to overcome the equid's natural, bred-in-the-bone fear of having something above and behind him - because that's where the big cats like leopards and lions attack from. Unfortunately, it's also where cart drivers and horse riders appear to the horse so the natural reaction was stark screaming panic, which makes it hard to get the horse to do anything useful.
In the Middle East, interestingly, almost exactly what you are describing actually happened. Native to that area was the Hemippi, a now-extinct equid (sometimes termed the Syrian Wild Ass) that was smaller than the average donkey (so not rideable at all) but a faster runner than even the average horse. Like many other equids, they could not be domesticated, but they could be bred with donkeys to produce the Kunga, the first known example of human-directed animal hybridization, which could be domesticated and used as a draft animal for wagons and the Sumerian War Carts we knew and 'loved' in Civ VI.
In a manner of speaking, Civ VII includes 'alternatives', but hides them. Thus, you can have 'cavalry' or chariots without any Horse resources in sight, they just aren't as good as if you had access to 'real' Horses. To me, that represents either that you are trading (smuggling) in horses on the quiet or using alternatives like donkey-hemippe hybrids from animals that don't appear on the map at all.
Donkeys, by the way, are depicted in Middle Eastern art being ridden as far back as 3000 BCE, well before any indication of domesticated horses being ridden. But the donkey's back is not strong enough to take the weight of a full-grown man for any length of time (and neither was a horse's, which was the other genetic manipulation done to them to make them really useful), so the 'donkey seat' right above the back legs was used - and also used by some of the first horse riders. This is much less stable and gives less control over the animal, so 'donkey cavalry' would not be able to charge at any speed, and the early donkey riders appear to have been scouts or messengers only.